Humanity Folds: Computers Have Cracked Texas Hold 'Em

You got to know when to fold 'em, humans.

Scientists have now created a program that has essentially solved the two-player limit version of Texas hold 'em poker. You can play against the program yourself online here.

This doesn't mean a machine always knows when you're bluffing and will beat a human every time, especially since so much luck and guile is at play in poker. What it means, statistically speaking, is that there is no significant chance to see if the computer's strategy is not the best within a human lifetime of play — 200 games per hour for 12 hours a day for 70 years. The team published a study about the program this week in Science.

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Solving this kind of poker is more than just fun and games, researchers say. "Our algorithm can attack a number of problems that have similar aspects to this game — adversarial settings where two players have antithetical goals against each other," says lead study author Michael Bowling, a computer scientist at the University of Alberta in Edmonton, Canada. "One application is in the realm of security. In the post-9/11 world, we want to set up security regimes that can protect strategic infrastructure like our airports and our port systems."

Heads Up

Computers have solved many so-called perfect-information games such as checkers and Connect Four, where all players can see everything that's happening in the game. (They haven't solved them all, though. Perfect information games like chess and go present too many possible moves for even supercomputers to crack through brute force calculations.) Poker, however, is a greater challenge. It's an imperfect-information game where players keep private knowledge of their cards, and use those secrets to add even more uncertainty to the game through strategies such as bluffing.

Bowling and his colleagues investigated the most popular variant of poker today, Texas hold 'em. They focused on the version that is heads-up (meaning it has just two players) and limit (with fixed bet-sizes and numbers of raises). Even with these limitations, an astounding 13.8 trillion potential moves can take place in heads-up limit Texas hold 'em. "Writing down what one can do at every decision point would take 10 terabytes, which is 1,000 times larger than the entire English-language version of Wikipedia," Bowling says.

Many researchers have been trying to solve heads-up limit Texas hold 'em, especially since the first Annual Computer Poker Competition in 2006. To reach this new milestone, Bowling and his colleagues "had 4,000 CPUs, with each CPU playing 6 billion hands of poker per second," he says. "Even with the CPUs altogether playing 24 trillion hands per second, it still took them two months to run the computations. By our estimates, we played more poker than all the games humans have ever played."

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The program the researchers developed to solve the game compresses data, so it requires significantly less memory to compute moves, and incorporates steps to find useful moves more quickly.

"This is the first time an imperfect-information game competitively played by humans has essentially been solved," says Tuomas Sandholm at Carnegie Mellon University in Pittsburgh, who did not take part in this study. The program also formally proved the common wisdom that the dealer holds a substantial advantage in the game.

Humans Beware

Other kinds of poker, such as Texas hold'em variants with no limit or more players, are far greater challenges with vastly more potential moves, Bowling cautions. No-limit heads-up Texas hold 'em has 10140 potential moves — that's a 1 with 140 zeroes behind it. "The universe only has about 1070 atoms," Bowling says. "So if you took each atom in the universe and put another universe's worth of atoms in it, that's how many decision points are involved with no-limit heads-up Texas hold'em."

Still, Bowling and other researchers want to push the limit with no-limit heads-up Texas hold'em. "Just because we can't solve the game doesn't mean that we can't develop a program that can beat humans," he says. "In the next few years, we should see that happen."

Building a machine that could win the World Series of Poker isn't the end goal, either. "Solving poker isn't the goal — it's more like a benchmark," Sandholm says. "The algorithms we as a field develop are not game-specific — they're not algorithms for just solving poker, but for imperfect-information games in general. There are applications for things like negotiations, security, politics, and even medicine."

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